Two S-wave eigenvectors of the Christoffel matrix need not exist in anisotropic viscoelastic media

Ludek Klimes


The 3*3*3*3 frequency-domain stiffness tensor is complex-valued in viscoelastic media. The 3*3 Christoffel matrix is then also complex-valued. We demonstrate that a complex-valued Christoffel matrix need not have all three eigenvectors at an S-wave singularity, and we thus cannot apply the eigenvectors to calculating the phase-space derivatives of the Hamiltonian function.


Attenuation, anisotropy, wave propagation, ray theory, ray tracing.

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Seismic Waves in Complex 3-D Structures, 30 (2020), 73-76 (ISSN 2336-3827, online at